Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation

A. Baskaran; J. S. Lowengrub; C. Wang; S. M. Wise

doi:10.1137/120880677

Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation

SIAM Journal on Numerical Analysis ◽

10.1137/120880677 ◽

2013 ◽

Vol 51 (5) ◽

pp. 2851-2873 ◽

Cited By ~ 46

Author(s):

A. Baskaran ◽

J. S. Lowengrub ◽

C. Wang ◽

S. M. Wise

Keyword(s):

Convergence Analysis ◽

Phase Field ◽

Second Order ◽

Splitting Scheme ◽

Convex Splitting ◽

Phase Field Crystal

Download Full-text

Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2017.07.012 ◽

2018 ◽

Vol 75 (6) ◽

pp. 1912-1928 ◽

Cited By ~ 13

Author(s):

Lixiu Dong ◽

Wenqiang Feng ◽

Cheng Wang ◽

Steven M. Wise ◽

Zhengru Zhang

Keyword(s):

Convergence Analysis ◽

Phase Field ◽

Numerical Scheme ◽

Three Dimensional ◽

Second Order ◽

Numerical Implementation ◽

Phase Field Crystal

Download Full-text

First and second order numerical methods based on a new convex splitting for phase-field crystal equation

Journal of Computational Physics ◽

10.1016/j.jcp.2016.09.053 ◽

2016 ◽

Vol 327 ◽

pp. 519-542 ◽

Cited By ~ 23

Author(s):

Jaemin Shin ◽

Hyun Geun Lee ◽

June-Yub Lee

Keyword(s):

Numerical Methods ◽

Phase Field ◽

Second Order ◽

Convex Splitting ◽

Phase Field Crystal

Download Full-text

Error estimates for second-order SAV finite element method to phase field crystal model

Electronic Research Archive ◽

10.3934/era.2020089 ◽

2021 ◽

Vol 29 (1) ◽

pp. 1735-1752

Author(s):

Liupeng Wang ◽

◽

Yunqing Huang ◽

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Error Estimates ◽

Phase Field ◽

Second Order ◽

Crystal Model ◽

Element Method ◽

Phase Field Crystal

Download Full-text

Linear second order energy stable schemes for phase field crystal growth models with nonlocal constraints

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2019.07.030 ◽

2020 ◽

Vol 79 (3) ◽

pp. 764-788 ◽

Cited By ~ 2

Author(s):

Xiaobo Jing ◽

Qi Wang

Keyword(s):

Crystal Growth ◽

Phase Field ◽

Growth Models ◽

Second Order ◽

Order Energy ◽

Energy Stable Schemes ◽

Energy Stable ◽

Nonlocal Constraints ◽

Phase Field Crystal

Download Full-text

About one unified description of the first‐ and second‐order phase transitions in the phase‐field crystal model

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.6801 ◽

2020 ◽

Cited By ~ 1

Author(s):

Vladimir Ankudinov ◽

Ilya Starodumov ◽

Peter K. Galenko

Keyword(s):

Phase Transitions ◽

Phase Field ◽

Second Order ◽

Crystal Model ◽

Unified Description ◽

Phase Field Crystal

Download Full-text

First- and second-order energy stable methods for the modified phase field crystal equation

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2017.03.033 ◽

2017 ◽

Vol 321 ◽

pp. 1-17 ◽

Cited By ~ 14

Author(s):

Hyun Geun Lee ◽

Jaemin Shin ◽

June-Yub Lee

Keyword(s):

Phase Field ◽

Second Order ◽

Order Energy ◽

Energy Stable ◽

Phase Field Crystal

Download Full-text

A linearly second-order energy stable scheme for the phase field crystal model

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.01.017 ◽

2019 ◽

Vol 140 ◽

pp. 134-164 ◽

Cited By ~ 1

Author(s):

Shuaichao Pei ◽

Yanren Hou ◽

Bo You

Keyword(s):

Phase Field ◽

Second Order ◽

Order Energy ◽

Crystal Model ◽

Energy Stable ◽

Energy Stable Scheme ◽

Stable Scheme ◽

Phase Field Crystal

Download Full-text

A Second-Order Convex Splitting Scheme for a Cahn-Hilliard Equation with Variable Interfacial Parameters

Journal of Computational Mathematics ◽

10.4208/jcm.1611-m2016-0517 ◽

2017 ◽

Vol 35 (6) ◽

pp. 693-710 ◽

Cited By ~ 5

Author(s):

Xiao Li

Keyword(s):

Second Order ◽

Splitting Scheme ◽

Hilliard Equation ◽

Convex Splitting ◽

Cahn Hilliard Equation

Download Full-text

An efficient linear second order unconditionally stable direct discretization method for the phase-field crystal equation on surfaces

Applied Mathematical Modelling ◽

10.1016/j.apm.2018.11.012 ◽

2019 ◽

Vol 67 ◽

pp. 477-490 ◽

Cited By ~ 9

Author(s):

Yibao Li ◽

Chaojun Luo ◽

Binhu Xia ◽

Junseok Kim

Keyword(s):

Phase Field ◽

Second Order ◽

Discretization Method ◽

Unconditionally Stable ◽

Phase Field Crystal

Download Full-text

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

Journal of Computational Physics ◽

10.1016/j.jcp.2016.10.020 ◽

2017 ◽

Vol 330 ◽

pp. 1116-1134 ◽

Cited By ~ 51

Author(s):

Xiaofeng Yang ◽

Daozhi Han

Keyword(s):

Phase Field ◽

Second Order ◽

Crystal Model ◽

Energy Stable Schemes ◽

Energy Stable ◽

Phase Field Crystal

Download Full-text